Search results
Results from the WOW.Com Content Network
A deterministic Turing machine has a transition function that, for a given state and symbol under the tape head, specifies three things: the symbol to be written to the tape (it may be the same as the symbol currently in that position, or not even write at all, resulting in no practical change),
English: A deterministic algorithm that performs f(n) steps always finishes with an accept or reject state, and always finishes with the same result. A non-deterministic algorithm that is f(n) levels may return different values on different runs, and may never finish with an accept or reject state.
In computational complexity theory, the complexity class NTIME(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine which runs in time O(f(n)). Here O is the big O notation, f is some function, and n is the size of the input (for which the problem is to be decided).
Recall that NP can be seen as the class of problems where an all-powerful prover gives a purported proof that a string is in the language, and a deterministic polynomial-time machine verifies that it is a valid proof. We make two changes to this setup: Add randomness, the ability to flip coins, to the verifier machine.
A deterministic Turing machine is the most basic Turing machine, which uses a fixed set of rules to determine its future actions. A probabilistic Turing machine is a deterministic Turing machine with an extra supply of random bits. The ability to make probabilistic decisions often helps algorithms solve problems more efficiently.
If there is an algorithm (say a Turing machine, or a computer program with unbounded memory) that produces the correct answer for any input string of length n in at most cn k steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Formally ...
A multitape deterministic Turing machine can never provide more than a quadratic time speedup over a singletape machine. [ 1 ] Due to the Linear speedup theorem for Turing machines, multiplicative constants in the time bound do not affect the extent of DTIME classes; a constant multiplicative speedup can always be obtained by increasing the ...
NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. [2]